论文期刊

An efficient Galerkin spectral method for two-dimensional fractional nonlinear reaction-diffusion-wave equation




作者: Shimin Guo; Liquan Mei; Ying Li
发表/完成日期: 2017-11-15
期刊名称: Computers and Mathematics with Applications
期卷:
相关文章:
论文简介
The aim of this paper is to develop an efficient numerical treatment for the two-dimensional fractional nonlinear
reaction-diffusion-wave equation with the time-fractional derivative of order α (1 < α < 2). For this purpose, we
employ the alternating direction implicit (ADI) method based on the Crank-Nicolson scheme for the time stepping,
while we apply the Legendre-Galerkin spectral method for the space discretization. The stability and convergence
analysis are rigorously set up. In addition, the proposed method is extended to solve the time-fractional Klein-Gordon
and sine-Gordon models. Numerical experiments are included, which verifies the theoretical predictions.